How many miles of perimeter fencing in 725 acres?

Answer 1

It depends upon the shape of the area of 725 acres; the minimum length is a circle with an area of 725 acres:

1 acre = 1/640 square mile

→ 725 acre = 725 ÷ 640 sq miles = 725/640 miles²

Area circle = π × radius²

→ radius = √(Area/π)

Circumference = 2 × π × radius

= 2 × π × √(Area/π)

= √(4 × π × Area)

= √(4 × π × 725/640 miles²)

= √(145π/32) miles

≈ 3.773 miles

You will require at least approx 3.773 miles of Fencing to enclose an area of 725 acres.

ie the fencing will be greater than or equal to approx 3.773 miles - there is no upper limit to the amount of fencing you will need.

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An acre was define as the amount of and an ox could plough in a day and is the area of a furrow long

(a furlong = 1/8 mile) by a chain (= 1/80 mile).

If you scale this rectangle up to 725 acres, it will be √725 larger in each direction, ie it will be a rectangle (√725)/8 miles by (√725)/80 miles

→perimeter = 2 × ((√725)/8 + (√725)/80) miles

= (2 × √725)(10 + 1)/80 miles

= (11√725)/40 miles

≈ 7.405 miles

If you had 725 of the furlong by chain fields next to each other along the furlong side, it would form a rectangle 1 furlong by 725 chains which gives:

perimeter = 2 × (1/8 + 725 × 1/80) miles

= 726/40 miles

= 18 3/20 miles

= 18.15 miles.

If the 725 files were next to each other along the chain side, it for form a rectangle 1 chain by 725 furlongs which gives:

perimeter = 2 × (1/80 + 725 × 1/80) miles

= 7251/40 miles

= 181 11/40 miles

= 181.275 miles